A differential geometric description of crystals with continuous distributions of lattice defects and undergoing potentially large deformations
is presented. This description is specialized to describe discrete defects, i.e., singular defect distributions. Three isolated defects are
considered in detail: the screw dislocation, the wedge disclination, and the point defect. New analytical solutions are obtained for elastic
fields of these defects in isotropic solids of finite extent, whereby terms up to second order in strain, involving elastic constants up to third
order, are retained in the stress components. The strain measure used in the nonlinear elastic potential – a symmetric function, expressed in
material coordinates, of the inverse deformation gradient – differs from that used in previous solutions for crystal defects, and is thought to
provide a more realistic depiction of mechanics of large deformation than previous theory involving third-order Lagrangian elastic constants
and the Green strain tensor. For the screw dislocation and wedge disclination, effects of core pressure and/or possible contraction along the
defect line are considered, and radial displacement contributions arise that are absent in the linear elastic solution, affecting dilatation. Stress
components are shown to differ from those of linear elastic solutions near defect cores. Volume change from point defects is strongly
affected by elastic nonlinearity.